The Absorptive Spectra Of Semiconductor Quantum Dot

It is a long time for people to study the optical properties of semiconductor quantum dot. A system composed of quantum dot can not be isolated from the outer circumstance, which means the effect of circumstance should be considered when dealing with the movement or process of particles in quantum dot. So, the purpose of this paper is to study the effects of circumstance (phonon's vibration) to the absorption spectra of the optical absorption process in semiconductor quantum dot.Most of current research work studies the properties of quantum dot by using numerical method. It is not visible enough or with less applicability. It is difficult for the numerical method to analog with the smaller parameters, even disabled for the situations that close to the critical point. So, we take a perturbation method based on unitary transformation to study the optical absorption process, in order to get the analytical expression result of the absorptive spectra.For a system made up of semiconductor quantum dot, the transition from valence band to conduction band could occur after the electrons in valence band absorbed the photons' energy in absorption process, in the meantime, it also be affected by the vibration of phonons. Therefore, this system can be described by as a two-level system coupled with phonons.In our paper, optical absorption properties of semiconductor quantum dot are studied by means of the perturbation approach and solving the Heisenberg's equations of motion. First of all, the Hamiltonian H of SBM is changed to H′by the means of unitary transformation. Then the HamiltonianH′can be divided into three parts: H 0′, H 1′and H 2′. The advantage of this method is: H 1′and H 2′are small enough which convince us to do the perturbation approximation. And then, equilibrium correlation function which relate with the optical conductivity, can be got via solving the Green's Function equation chain. At last, the analytical expression of optical conductivity is obtained by using the Fourier transformation. According to the expression of optical conductivity, we illustrate the absorption spectra, from which we get the conclusions: Our result shows clearly both the line shape and the peak position of the optical conductivity spectrum. The peak position of optical conductivity moves to lower photon energy as the coupling constant increases and the peak position is not directly corresponding to the energy difference between the ground state and the lowest-lying excited state in QD. The increase of coupling constant enhances the shift of peak position of optical conductivity spectrum and the coupling strength has stronger effect on the process of electron transition for larger bare tunneling energy.The main idea of this paper is to discuss the influences of electron-phonon interaction to the absorption progress in semiconductor quantum dot. We study these properties under the situations of zero temperature, weak electron-phonon coupling and taking Ohmic spectral density.The program is just to consider the transitions occur between two lowest level ranges and ignore the excited state transition's effect to the absorptive spectra. We will consider multi-excited states'effects within the range of calculation possibilities in the further study. And, our current research is to calculate the transitions in three levels.